## Regression models of placement outcomes
library(tidyverse)
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library(cowplot)
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library(broom)
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library(forcats)
library(rstanarm)
## Loading required package: Rcpp
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## rstanarm (Version 2.18.2, packaged: 2018-11-08 22:19:38 UTC)
## - Do not expect the default priors to remain the same in future rstanarm versions.
## Thus, R scripts should specify priors explicitly, even if they are just the defaults.
## - For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores())
## - Plotting theme set to bayesplot::theme_default().
options(mc.cores = parallel::detectCores() - 2)
## bayesplot makes itself the default theme
theme_set(theme_minimal())
library(tictoc)
library(assertthat)
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## has_name
## Suppress messages when generating HTML file
knitr::opts_chunk$set(message = FALSE)
source('../R/predictions.R')
source('../R/posterior_estimates.R')
data_folder = '../data/'
output_folder = '../output/04_'
paper_folder = '../paper/'
# cluster_distances = read_csv(str_c(data_folder,
# '00_k9distances_2019-03-15.csv')) %>%
# count(cluster = cluster, average_distance = avgDist) %>%
# mutate(cluster = as.character(cluster))
#
# ggplot(cluster_distances, aes(cluster, scale(average_distance))) +
# geom_label(aes(label = n, fill = n, size = n), color = 'white')
load(str_c(data_folder, '02_parsed.Rdata'))
univ_df = read_rds(str_c(data_folder, '03_univ_net_stats.rds')) #%>%
# left_join(cluster_distances)
individual_df = individual_df %>%
left_join(univ_df, by = c('placing_univ_id' = 'univ_id')) %>%
## Use the canonical names from univ_df
select(-placing_univ) %>%
## Drop NAs
# filter(complete.cases(.))
filter_at(vars('permanent', 'aos_category',
'graduation_year', 'prestige',
'community', 'cluster_label',
'gender', 'frac_w',
'frac_high_prestige', 'total_placements'),
all_vars(negate(is.na)(.))) %>%
rename(cluster = cluster_label) %>%
mutate(perc_w = 100*frac_w,
perc_high_prestige = 100*frac_high_prestige)
## Variables to consider: aos_category; graduation_year; placement_year; prestige; out_centrality; cluster; community; placing_univ_id; gender; country; perc_w; total_placements
## Giant pairs plot/correlogram ----
## perc_high_prestige, out_centrality, and prestige are all tightly correlated
## All other pairs have low to moderate correlation
individual_df %>%
select(permanent, aos_category, aos_diversity, perc_high_prestige,
graduation_year, placement_year, prestige,
in_centrality, out_centrality, community,
cluster, #average_distance,
gender, country, perc_w,
total_placements) %>%
mutate_if(negate(is.numeric), function(x) as.integer(as.factor(x))) %>%
mutate_at(vars(in_centrality, out_centrality), log10) %>%
# GGally::ggpairs()
cor() %>%
as_tibble(rownames = 'Var1') %>%
gather(key = 'Var2', value = 'cor', -Var1) %>%
ggplot(aes(Var1, Var2, fill = cor)) +
geom_tile() +
geom_text(aes(label = round(cor, digits = 2)),
color = 'white') +
scale_fill_gradient2()
## No indication that AOS diversity has any effect
ggplot(individual_df, aes(aos_diversity, 1*permanent)) +
geom_point() +
geom_smooth(method = 'loess')
## And not for fraction of PhDs awarded to women women, either
ggplot(individual_df, aes(frac_w, 1*permanent)) +
geom_point() +
geom_smooth(method = 'loess')
## Descriptive statistics ----
## Individual-level variables (all discrete)
desc_1_plot = individual_df %>%
select(permanent, aos_category,
graduation_year, placement_year,
gender) %>%
gather(key = variable, value = value) %>%
count(variable, value) %>%
mutate(variable = str_replace_all(variable, '_', ' ')) %>%
ggplot(aes(fct_rev(value), n, group = variable)) +
geom_col(aes(fill = variable), show.legend = FALSE) +
scale_fill_brewer(palette = 'Set1') +
xlab('') +
coord_flip() +
facet_wrap(vars(variable), scales = 'free', ncol = 3)
## Warning: attributes are not identical across measure variables;
## they will be dropped
desc_1_plot
ggsave(str_c(output_folder, 'descriptive_1.png'),
desc_1_plot,
height = 2*2, width = 2*3, scale = 1.5)
## Program-level categorical
desc_2_plot = individual_df %>%
select(prestige, country,
community, cluster) %>%
gather(key = variable, value = value) %>%
count(variable, value) %>%
ggplot(aes(fct_rev(value), n, group = variable)) +
geom_col(aes(fill = variable), show.legend = FALSE) +
scale_fill_viridis_d() +
xlab('') +
coord_flip() +
facet_wrap(vars(variable), scales = 'free', ncol = 3)
desc_2_plot
ggsave(str_c(output_folder, 'descriptive_2.png'),
desc_2_plot,
height = 2*2, width = 2*2, scale = 1.5)
## Program-level continuous variables
# individual_df %>%
# select(frac_w, total_placements, perm_placement_rate) %>%
# gather(key = variable, value = value) %>%
# group_by(variable) %>%
# summarize_at(vars(value),
# funs(min, max, mean, median, sd),
# na.rm = TRUE)
program_cont = individual_df %>%
mutate(in_centrality = log10(in_centrality)) %>%
select(`women share` = frac_w,
`total placements` = total_placements,
`permanent placement rate` = perm_placement_rate,
`AOS diversity (bits)` = aos_diversity,
`hiring centrality (log10)` = in_centrality) %>%
gather(key = variable, value = value)
desc_3_plot = ggplot(program_cont, aes(value)) +
geom_density() +
geom_rug() +
geom_vline(data = {program_cont %>%
group_by(variable) %>%
summarize(mean = mean(value))},
aes(xintercept = mean,
color = 'mean')) +
geom_vline(data = {program_cont %>%
group_by(variable) %>%
summarize(median = median(value))},
aes(xintercept = median,
color = 'median')) +
scale_color_brewer(palette = 'Set1',
name = 'summary\nstatistic') +
facet_wrap(~ variable, scales = 'free', ncol = 3) +
theme(legend.position = 'bottom')
desc_3_plot
ggsave(str_c(output_folder, 'descriptive_3.png'),
desc_3_plot,
height = 2*2, width = 2*3.5, scale = 1.5)
plot_grid(desc_1_plot,
desc_2_plot,
desc_3_plot,
align = 'v', axis = 'lr', ncol = 1,
labels = 'AUTO',
hjust = -2
)
ggsave(str_c(output_folder, 'descriptive.png'),
height = 6.5*2, width = 4*2, scale = 1.5)
ggsave(str_c(paper_folder, 'fig_descriptive.png'),
height = 6.5*2, width = 4*2, scale = 1.5)
## Model -----
model_file = str_c(data_folder, '04_model.Rds')
if (!file.exists(model_file)) {
## ~700 seconds
tic()
model = individual_df %>%
mutate(prestige = fct_relevel(prestige, 'low-prestige'),
country = fct_relevel(country, 'U.S.')) %>%
stan_glmer(formula = permanent ~
(1|aos_category) +
gender +
(1|graduation_year) +
(1|placement_year) +
1 +
aos_diversity +
(1|community) +
(1|cluster) +
# average_distance +
log10(in_centrality) +
total_placements +
perc_w +
country +
prestige,
family = 'binomial',
## Priors
## Constant and coefficients
prior_intercept = cauchy(0, 2/3, autoscale = TRUE), ## constant term + random intercepts
prior = cauchy(0, 2/3, autoscale = TRUE),
## error sd
prior_aux = cauchy(0, 2/3, autoscale = TRUE),
## random effects covariance
prior_covariance = decov(regularization = 1,
concentration = 1,
shape = 1, scale = 1),
seed = 1159518215,
adapt_delta = .99,
chains = 4, iter = 4000)
toc()
write_rds(model, model_file)
} else {
model = read_rds(model_file)
}
prior_summary(model)
## Priors for model 'model'
## ------
## Intercept (after predictors centered)
## ~ cauchy(location = 0, scale = 0.67)
##
## Coefficients
## ~ cauchy(location = [0,0,0,...], scale = [0.67,0.67,0.67,...])
## **adjusted scale = [0.67,0.67,1.70,...]
##
## Covariance
## ~ decov(reg. = 1, conc. = 1, shape = 1, scale = 1)
## ------
## See help('prior_summary.stanreg') for more details
## Check ESS and Rhat
## Rhats all look good. ESS a little low for grad years + some sigmas
model %>%
summary() %>%
as.data.frame() %>%
rownames_to_column('parameter') %>%
select(parameter, n_eff, Rhat) %>%
# knitr::kable()
ggplot(aes(n_eff, Rhat, label = parameter)) +
geom_point() +
geom_vline(xintercept = 3000) +
geom_hline(yintercept = 1.01)
if (require(plotly)) {
plotly::ggplotly()
}
## Variables w/ fewer than 3000 effective draws
## covariance on random intercepts; log posterior
model %>%
summary() %>%
as.data.frame() %>%
rownames_to_column('parameter') %>%
as_tibble() %>%
filter(n_eff < 3000) %>%
select(parameter, n_eff)
## # A tibble: 2 x 2
## parameter n_eff
## <chr> <dbl>
## 1 Sigma[community:(Intercept),(Intercept)] 1933
## 2 log-posterior 1807
## Check predictions
pp_check(model, nreps = 200)
pp_check(model, nreps = 200, plotfun = 'ppc_bars')
## <https://arxiv.org/pdf/1605.01311.pdf>
pp_check(model, nreps = 200, plotfun = 'ppc_rootogram')
pp_check(model, nreps = 200, plotfun = 'ppc_rootogram',
style = 'hanging')
## 90% centered posterior intervals
estimates = posterior_estimates(model, prob = .9)
## Estimates plot
estimates %>%
filter(entity != 'intercept',
group != 'placement_year') %>%
## posterior_estimates() already exponentiates estimates
mutate_if(is.numeric, ~ . - 1) %>%
ggplot(aes(x = level, y = estimate,
ymin = lower, ymax = upper,
color = group)) +
geom_hline(yintercept = 0, linetype = 'dashed') +
geom_pointrange() +
scale_color_viridis_d(name = 'covariate\ngroup') +
xlab('') + #ylab('') +
scale_y_continuous(labels = scales::percent_format(),
name = '') +
coord_flip(ylim = c(-1, 1.75)) +
facet_wrap(~ entity, scales = 'free') +
theme(legend.position = 'bottom')
ggsave(str_c(output_folder, 'estimates.png'),
width = 8, height = 4.5,
scale = 1.5)
ggsave(str_c(paper_folder, 'fig_reg_estimates.png'),
width = 8, height = 4.5,
scale = 1.5)
estimates %>%
filter(entity != 'intercept',
group != 'placement_year') %>%
select(group, level, estimate, lower, upper) %>%
mutate_if(is.factor, as.character) %>%
arrange(group, level) %>%
knitr::kable(format = 'latex',
digits = 2,
booktabs = TRUE,
label = 'estimates',
caption = 'Estimated regression coefficients. Lower and upper columns give the left and right endpoints, respectively, of the centered 90\\% posterior intervals.') %>%
write_file(path = str_c(output_folder, 'estimates.tex'))
## Marginal effects for gender and prestige ----
## <https://stackoverflow.com/questions/45037485/calculating-marginal-effects-in-binomial-logit-using-rstanarm>
marginals = function (dataf, model, variable,
ref_value = 0L,
alt_value = 1L) {
variable = enquo(variable)
all_0 = mutate(dataf, !!variable := ref_value)
all_1 = mutate(dataf, !!variable := alt_value)
pred_0 = posterior_linpred(model, newdata = all_0,
transform = TRUE)
pred_1 = posterior_linpred(model, newdata = all_1,
transform = TRUE)
marginal_effect = pred_1 - pred_0
return(marginal_effect)
}
marginals_gender = individual_df %>%
## posterior_linpred raises an error when there are any NAs, even in columns that aren't used by the model
select(-city, -state) %>%
marginals(model, gender,
ref_value = 'm',
alt_value = 'w')
apply(marginals_gender, 1, mean) %>%
quantile(probs = c(.05, .5, .95))
## 5% 50% 95%
## 0.06521784 0.10415260 0.14256224
# 5% 50% 95%
# 0.06891015 0.10920815 0.14868667
marginals_prestige = individual_df %>%
select(-city, -state) %>%
marginals(model, prestige, 'low-prestige', 'high-prestige')
apply(marginals_prestige, 1, mean) %>%
quantile(probs = c(.05, .5, .95))
## 5% 50% 95%
## 0.07925371 0.12297629 0.16722014
# 5% 50% 95%
# 0.07614823 0.11987722 0.16543114
marginals_canada = individual_df %>%
select(-city, -state) %>%
marginals(model, country, 'U.S.', 'Canada') %>%
apply(1, mean) %>%
quantile(probs = c(.05, .5, .95))
## Schools in certain communities ----
comms_of_interest = c(3, 5, 12, 37, 54,
8, 27, 38, 43) %>%
as.character()
univ_df %>%
filter(community %in% comms_of_interest,
total_placements > 0) %>%
select(community, name = univ_name,
total_placements, perm_placement_rate) %>%
mutate(community = fct_relevel(community, comms_of_interest),
perm_placement_rate = scales::percent_format()(perm_placement_rate)) %>%
arrange(community, name) %>%
knitr::kable(format = 'latex',
# digits = 2,
booktabs = TRUE,
label = 'comms',
caption = 'Universities in selected topological communities. Only universities with at least 1 placement in the data are shown.') %>%
write_file(path = str_c(output_folder, 'comms.tex'))
sessionInfo()
## R version 3.5.1 (2018-07-02)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS 10.14.6
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## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
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## other attached packages:
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## [5] Rcpp_1.0.1 broom_0.5.2 cowplot_1.0.0 forcats_0.4.0
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## [52] magrittr_1.5 loo_2.1.0 bayesplot_1.6.0
## [55] Matrix_1.2-17 fansi_0.4.0 munsell_0.5.0
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## [73] ps_1.3.0 pillar_1.3.1 igraph_1.2.4
## [76] boot_1.3-20 markdown_0.9 shinystan_2.5.0
## [79] codetools_0.2-16 reshape2_1.4.3 stats4_3.5.1
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